Assertion (A): The sum of the series with the nth term,

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Q.
Assertion (A): The sum of the series with the nth term, $a_{n} = 9 - 5 n$ is –465 when number of terms, n = 15.

Reason (R): The sum of first n terms of an AP is given by $S_{n} = n / 2 [2 a + (n - 1) d]$

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false

4 A is false, but R is true.

Ans.
(1)

$G i v e n n t h t e r m a_{n} = 9 - 5 n F i r s t t e r m, a_{1} = 9 - 5 \times 1 = 4 \Rightarrow a = 4 L a s t t e r m, a_{15} = 9 - 5 \times 15 = 9 - 75 = - 66 S u m o f t h e s e r i e s : S_{15} = 15 / 2 (a + l) = 15 / 2 (4 - 66) = 15 / 2 (- 62) = 15 \times (- 31) = - 465 A l s o b y t h e f o r m u l a, S_{n} = n / 2 (2 a + (n - 1) d) = n / 2 (a + l)$

Solution

Q.
Assertion (A): The sum of the series with the nth term, $a_{n} = 9 - 5 n$ is –465 when number of terms, n = 15.

Reason (R): The sum of first n terms of an AP is given by $S_{n} = n / 2 [2 a + (n - 1) d]$

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false

4 A is false, but R is true.

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Solution

Q. Assertion (A): The sum of the series with the nth term, an = 9–5n is –465 when number of terms, n = 15. Reason (R): The sum of first n terms of an AP is given by Sn=n/2[2a+(n-1)d]

1 Both A and R are true, and R is the correct explanation of A.

2 Both A and R are true, but R is not the correct explanation of A

3 A is true, but R is false

4 A is false, but R is true.

Ans. (1) Given nth term an=9-5nFirst term, a1=9-5×1=4⇒a=4Last term, a15=9-5×15=9-75=-66Sum of the series: S15=15/2(a+l)=15/2(4-66)=15/2(- 62)=15×(- 31)=-465Also by the formula,Sn=n/2(2a+(n-1)d)=n/2(a+l)

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Q.
Assertion (A): The sum of the series with the nth term, $a_{n} = 9 - 5 n$ is –465 when number of terms, n = 15.

Reason (R): The sum of first n terms of an AP is given by $S_{n} = n / 2 [2 a + (n - 1) d]$